The local tri club holds a 40K TT once a month that I have recently started participating in to monitor my progress sans power meter. My bike specific fitness is lacking, but my cardio respiratory system is pretty good so I'm able to push pretty hard. Both times I have gotten muscle soreness felt immediately after crossing the line and leaving aero position to cool down in my upper hamstring. The soreness seems to be located to a 5in square area just below my buttocks near the hamstring insertion. The soreness will stay for around a week before it subsides. This has happened at both time trials. I have never had this happen even after a very intense workout.

Abridged version: Can DOMs like symptoms onset immediately after exercise and not the day after as usual?

By definition that is not DOMS, sounds like a strain

I understand what the definition of DOMs is. So I understand what I experienced is not defined as such. I'm asking if we can experience similar symptoms to DOMs, but in a shorter onset. What ThisisIt experienced is more closely in line with what I felt. Almost as if I over accumulated lactic acid, and was slow to buffer out. By the second day it was 90% gone. Further contractions were not painful, just sore.
Maybe I should have more correctly titled the post "Is it possible to get DOMs like symptoms immediately following exercise"
I grew up playing soccer and have experienced muscle strains before, and this was, in my opinion, not it. The fact that the phenomenon was bilateral, and showed up twice confirms to me it was probably not a strain.

What is the heel-to drop on your usual shoes compared to your flats? Lots of posts and information about the 'perils' of too rapidly moving to flats.

I use a variety of shoes:

normal training shoes - Nike Pegasus (heel drop 10mm), long - Hoka Stinson, although I could still use my pegs if I wanted to
racing - normally Asics Noosa heel drop 10mm

The racing flats I just bought are Asics Hyper Speed (heel drop around 6mm). They are probably only going to be good for 5/10km races sprints/ODs. Was hoping to use them in 70.3s, but obviously that's not a good idea at this moment in time.

I'm definitely not racing in the hyper speeds this weekend. Prefer to race in my Noosas, but I'm now wondering if I should go for the Hokas which I really don't want to. They are slow as..

^^This. "delayed onset muscle soreness"

Sounds like you just went too far to early in shoes with much less toe/heel drop. Less heel drop = more extension of your calf muscle. If you're accustomed to a different position the muscle won't be adapted for this and you should ease into it to avoid injury. This, in my opinion, was the biggest problem for minimalist running shoes - people switching without considering the implications.
I started using minimalist running shoes several years ago and went from shoes with 10-12mm of drop and serious cushioning to zero drop and zero cushioning. I did take the transition period cautiously, starting by running just 400m and working up slowly to 10km+ over a period of a few months. Even so, I had quite a bit of calf tightness and soreness similar to what you describe though I never got anything I'd consider an injury. Thankfully I stuck with it and now run all distances, including IM marathon in zero drop minimalist shoes, more comfortably than I ever did before. I would think your calves will need several days to recover so the weekend race could be an issue, hopefully not.
Don't let this put you off the racing flats. Just give it a little time to get used to them. I wouldn't think you'll need months as drastic a change as I described, but jumping straight in at a 10km training run is not wise.

Good luck!

P.S. The D in DOMs is Delayed. So if it's immediate, it's not DOMs! ;)
However the adaptation discomfort I described above seemed to come on during or immediately after the run as tightness which remained for some time afterwards and seemed to mutate into typical DOMs over the following 48hrs. IIRC stretching the calf and achilles during and after the run seemed to help.